This paper describes how to create ex-ante expectation for generalized trend-following rules. This report first study the effect of trend-following rules applied to random data with varying degrees of drift and autocorrelation. There is a positive relationship between drift, autocorrelation and the theoretically extractable Sharpe ratio for a trend following strategy. Drift is more important, since it is theoretically unbounded, but strong auto-correlation can create positive returns in the absence of long term drift. The realized Sharpe ratio of a trend strategy is proportional to the absolute drift and auto-correlation of a market above a threshold. From a practical perspective, this means that anyone engaging in trend following strategies, should expect to generate positive returns if the drift is strong enough or if there is enough autocorrelation. Conversely, when there is no drift or auto-correlation, trend-following is not profitable. There is a strong preference for slower strategies under drift and transaction costs. Returns are compared to actual markets and indices of active traders (managed futures) and a high correlation is detected to the results in this paper. Trend-following should never be applied to a single market on a stand-alone basis. That said, even portfolios of trend following strategies have low expected Sharpe, especially so when the systems generated correlated trades. In the end, trend-following does not necessarily need uncorrelated markets, but rather uncorrelated system-market returns. A nuance that is often lost.

Notable quotations from the academic research paper:

"In this report, the author has derived and verified the importance of auto-correlation and risk-adjusted drift for simple trend based strategies. After having reviewed the facts, auto-correlation for actual markets is close to zero (at least over the last 15 years) and most markets have a low drift. Thus, any return generated from medium to long-term trend following strategies is mostly due to market drift, rather than auto-correlation.

Trend-following, on a stand-alone basis, is a low Sharpe strategy, with an expected per-market Sharpe of approximately 0.15, depending on the drift of the underlying market. From there, the author performs an analysis in terms of market / system-market correlation which allows a predication of the expected Sharpe ratio for portfolios of strategies.

Trend following depends, not only on having a low market correlation, but is more dependent on having a low correlation between trading-systems. To some extent, this is one of the reasons for why trend-following is sometimes referred to as a portfolio effect. Most successful trend-following results have been recorded in diversified portfolios, rather than for single market traders.

This report rests on the assumption that it is correct to approximate the result and correlation for other trend strategies with a long term momentum strategy. This is not always the case as there are trend strategies that are not perfectly correlated to the tested strategies.

When compared to actual hedge fund results, this report finds that two (Barclay and Credit Suisse) out of three indices tested, mirrors the results of a correlation driven reduction in the realized Sharpe. Larger managers, in more concentrated indices (Newedge CTA), have managed to generate better results. As a first approximation, attributing this to higher concentration to liquid markets (equities and fixed income) as well as potentially having access to diversifying strategies seems prudent.

For traders that using trend-following strategies, it would seem prudent to continue to look for uncorrelated markets/trading systems while trying to explicitly understand why a market would have a persistent auto-correlation and/or a high risk adjusted drift.

A more extreme version would be to build a large number of uncorrelated systems and apply them to a set of markets. There, despite having a long expected Sharpe ratio for each system, it is still possible to create diversifying return streams. This may no longer be a trend-following strategy though."

A new monetary theory is set out to resolve the "Uncovered Interest Parity (UIP)" Puzzle. It explores the possibility that liquidity properties of money and nominal bonds can account for the puzzle. A key concept in our model is that nominal bonds carry liquidity premia due to their medium of exchange role as either collateral or means of payment. In this framework no-arbitrage ensures a positive comovement of real return on money and nominal bonds. Thus, when inflation in one country becomes relatively lower, i.e., real return on this currency is relatively higher, its nominal bonds should also yield higher real return. We show that their nominal returns can also become higher under the economic environment where collateral pledgeability and/or liquidity of nominal bonds and/or collateralized credit based transactions are relatively bigger. Since a currency with lower inflation is expected to appreciate, the high interest currency does indeed appreciate in this case, i.e., the UIP puzzle is no longer an anomaly in our model. Our liquidity based theory can in fact help understanding many empirical observations that risk based explanations find difficult to reconcile with.

Notable quotations from the academic research paper:

"The vast majority of the literature on UIP puzzle is empirical, and very few theoretical attempts have been made to tackle the puzzle. Even among the theoretical literature, no consensus seems to have been reached. For instance, most prevailing theories revolve around the idea that the failure of the UIP has a close connection with the way the risk premium behaves. Nevertheless, many recent studies have become critical of these risk-based explanations. To that end, we take an alternative approach in this paper that the UIP violation might be attributed to endogenous liquidity properties of money and bonds.

In our microfounded monetary model of international asset pricing, the UIP does not have to hold uniformly. In particular, the negative relationship between anticipated inflation and nominal bond yield is shown to be sufficient for the UIP deviation. Crucially, our framework implies that nominal bonds must exhibit relatively high enough liquidity premia in order to guarantee the sufficient condition. We show in the model that the sufficiently higher liquidity premia of bonds can be indeed achieved when the portion of collaterlized-credit-transaction-based pairwise meetings is large and/or the pledgeability of bonds as collateral is high and/or exogenous illiquidity discount on bonds as a direct means of payment is low.

One may question if our framework where bonds exhibit as high liquidity premia as money is empirically substantive. One can then address potential concerns. First, not every nominal bonds, especially those issued by emerging economies, are same as the U.S. Treasury bonds. Second, the bond liquidity is surely time-varying, e.g., extreme dry-up of bond liquidity during the recent liquidity crunch episode.

Very interestingly, these two issues are precisely what leads to the non-uniform UIP deviation in our framework. Put it differently, our model implies that the sufficient condition for the UIP deviation cannot be met whenever bonds are not liquid enough. This bond illiquidity is one of the defining characteristics of emerging market bonds and the liquidity crisis. Thus, our model predicts that the UIP should be confined to emerging economies and the liquidity crunch period. These two predictions are well supported by prominent empirical studies."

Several studies have attributed the high excess returns of the momentum strategy in the equity market to investor behavioral biases. However, whether momentum effects occur because of investor underreaction or because of investor overreaction remains a question. Using a simple model to illustrate the linkage between idiosyncratic volatility and investor overreaction as well as the stock turnover as another measure of overreaction, I present evidence that supports the investor overreaction explanation as the source of momentum effects. Furthermore, I show that when investor overreaction is low, momentum effects are more due to industries (industry momentum) rather than stocks.

Notable quotations from the academic research paper:

"The existence of significantly positive excess returns from momentum strategies is well established in the literature. However, there is no consensus over what drives these returns. Finding a risk-based explanation for the momentum effects is a tremendously difficult task and momentum constitutes perhaps "the toughest challenge for rational theories of the cross-section of stock returns" (Nagel, 2001). As an alternative, behavioral theories of momentum effects have been suggested by a number of researchers.

The models in this behavioral literature can be divided into two camps: those that characterized price momentum as investor underreaction and those that view it as an investor overreaction to information.

The contributions of this paper are as follows. First, I provide a channel for the contribution of investor overreaction to the idiosyncratic volatility of stocks. Second, I present empirical evidence of the relationship between momentum effects, idiosyncratic volatility and stock turnover. I argue that these results are consistent with the overreaction explanation of momentum effects and also provide a clearer explanation for the connection between momentum and idiosyncratic volatility. Third, I shed some light on the relationship between stock momentum and industry momentum and show that the contribution of the industries in the momentum varies with the level of firm-specific information which is proxied by idiosyncratic volatility.

In this paper, I verify that the momentum effect is stronger among stocks with higher idiosyncratic volatility. I then examine an alternative null hypothesis that does not rely on mispricing or limits to arbitrage. I employ a simple model and show that idiosyncratic volatility is related to the investor overreaction. By introducing the relationship between idiosyncratic volatility and overreaction, I conclude that the higher momentum effect among stocks with higher idiosyncratic volatility is due to investor overreaction. I, therefore, provide support for the overreaction explanation of momentum effects.

In this study, I analyze the relationship between industry and stock momentum from a different perspective. I show that industry momentum contributes more to stock momentum when idiosyncratic volatility is low. Among stocks with high idiosyncratic volatility, most of the momentum returns are driven by stocks rather than industries. This is consistent with the overreaction explanation: when idiosyncratic volatility is low, it implies that investors' overreaction is lower, so momentum returns (which is lower than those of the higher idiosyncratic volatility stocks) are more due to industry momentum. When idiosyncratic volatility is high, there is higher investor overreaction to the stock level information and most of the momentum effect is solely individual security momentum rather than industry momentum."

Value strategies exhibit a large positive beta if contemporaneous market excess returns are positive, and a small beta if contemporaneous market excess returns are negative. Value also has a large positive beta after bear markets, but a small beta after bull markets. These facts hold for equity-value strategies in 21 countries, and to a lesser extent for three non-equity-value strategies. Betas conditional on contemporaneous market returns are able to capture expected return variation associated with the book-to-market ratio. These betas partially explain the value premium, and are related to a larger cash-flow risk of value strategies.

Notable quotations from the academic research paper:

"Value strategies exhibit asymmetric betas: a large and positive up-market beta when the contemporaneous market excess returns are positive, and a small or negative down-market beta when the contemporaneous market excess returns are zero or negative. Value strategies also exhibit time-varying betas: after a string of good market returns, or a bull market, value has a small negative bull-market beta. After a string of poor market returns, value has a large positive bear-market beta. Asymmetric betas and time-varying betas also exist for international equity-value strategies, and to a lesser extent, in three non-equity-value strategies.

Asymmetric betas and time-varying betas are plausibly linked through mean-reversion of market returns. Value has a large positive beta in bear markets when market returns have been low. Because market returns tend to mean-revert, expected market returns are high when realized returns have been low. Therefore, value has a large positive beta when expected market returns are high. Value also has a small negative beta when expected market returns are low. Taken together, the time-varying betas combined with mean-reverting market returns translate into asymmetric contemporaneous betas.

Conditional market exposures shed light on the mechanism of value strategies. A decomposition of beta into its cash-flow and discount-rate components reveals asymmetric betas mostly come from cash-flow betas, consistent with the idea that value securities have higher cash-flow risk."

Moskowitz, Ooi, and Pedersen (2012) show that time series momentum delivers a large and significant alpha for a diversified portfolio of various international futures contracts over the 1985 to 2009 period. Although we confirm these results with similar data, we find that their results are driven by the volatility-scaled returns (or the so-called risk parity approach to asset allocation) rather than by time series momentum. The alpha of time series momentum monthly returns drops from 1.27% with volatility-scaled weights to 0.41% without volatility scaling, which is significantly lower than the cross-sectional momentum alpha of 0.95%. Using volatility-scaled positions, the cumulative return of a time series momentum strategy is higher that that of the buy-and-hold strategy; however, timeseriesmomentuman buy-and-hold offer similar cumulative returns if they are not scaled by volatility. The superior performance of the time series momentum strategy also vanishes in the more recent post-crisis period of 2009 to 2013.

Notable quotations from the academic research paper:

"We revisit the findings of MOP (Moskowitz, Ooi, and Pedersen 2012 time series momentum strategy) using 55 futures contracts over the 1985to 2013 period. One special procedure used by MOP is that they scale the returns of the different futures contracts by a simple lagged estimate of volatility. In particular, an asset with a lower volatility will take a greater position size and have a higher weight in the portfolio. Using the same period as MOP, 1985-2009, and also volatility-scaling returns, we find similar results: A portfolio of 55 futures contracts based on the prior 12-month momentum offers an alpha of 1.27% per monthand the alphas of all the individual contracts (except one) are positive with an average of 1.31%. However, if we use unscaled equal-weighted returns, the portfolio alpha and the average individual alpha drop to 0.41% and 0.42%, respectively.

More specifically, MOP scale the volatility of each individual futures contract to correspond to the volatility of an average stock by effectively leveraging the positions. When we scale the futures contracts toa lower (higher) volatility, we obtain smaller (larger) alphas, and scaling the buy-and-hold strategy produces similar results. Thus the magnitude of the TSMOM strategy appears to be largely due to leveraging a strategy which happened to generate a positive alpha. Without volatility scaling, the monthly time series momentum returns underperform the cross-sectional momentum strategy.

Moreover, while we find a positive alpha when applying a TSMOM (time series momentum) strategy to individual contracts, the individual contract returns do not generally outperform a buy-and-hold futures strategy. Specifically, TSMOM offers higher profits than buy-and-hold for 29 (out of 55) contracts using unscaled returns, and 31 contracts using volatility-scaled returns.

MOP also show that time series momentum profits are larger than those from the cross-sectional momentum (XSMOM) strategy of Jegadeesh and Titman (1993). In contrast, examining the foreign exchange market only, Menkoff et al. (2012) find that the TSMOM strategy is less profitable than the XSMOM strategy. We note that when implementing the TSMOM, Menkoff et al. do not volatility-scale their results. In our study, we show that the alpha of the XSMOM, 0.95%, lies between the alphas obtained from the TSMOM using equal (non-volatility-scaled) and volatility-scaled weights. Therefore, the different weighting schemes may explain the conflicting conclusions of MOP and Menkoff et al.

The volatility scale used by MOP is similar to the so-called risk parity approach to asset allocation. A risk parity portfolio is an equally weighted portfolio, where the weights refer to risk (proxied by standard deviation in MOP) rather than dollar amount invested in each asset (Kazemi, 2012). Risk parity balances a portfolio by increasing (decreasing) the weights of low (high) risk assets and using leverageto attain higher portfolio returns.

We also examine the results for several sub-periods: pre and post-2001, and following the financial crisis, 2009-2013. The choice of 2001 is based on a potential structural break in commodity futures markets around the passage of the Commodity Futures Modernization Act (CFMA) in December 2000. We show that the superior performance of TSMOM is concentrated in the pre-2001 period. When we use more recent periods, we find that the performance of TSMOM is worse than that of a buy-and-hold strategy. These results are consistent with the increase in market quality documented for the equity market by Chordia, Roll, and Subrahmanyam (2011)."